Question

Find the coordinates of point P which lies along the directed segment from M(-4, 7) to N(12, -1) that partitions the segment into a ratio of 1:7.

Answer 1

To find the point P, we have to use the following formulas

$\begin{gathered} x=\frac{a}{a+b}(x_2-x_1)+x_1 \\ y=\frac{a}{a+b}(y_2-y_1)+y_1 \end{gathered}$

Where a = 1, b = 7, x1 = -4, x2 = 12, y1 = 7, and y2 = -1. Let's use these values to find each coordinate.

$\begin{gathered} x=\frac{1}{1+7}(12-(-4))+(-4)=\frac{1}{8}(16)-4=2-4=-2 \\ y=\frac{1}{1+7}(-1-7)+7=\frac{1}{8}(-8)+7=-1+7=6 \end{gathered}$

Hence, the coordinates of point P are (-2, 6).